Simulation of Wave Equation on Manifold using DEC

TL;DR

This paper presents a discrete exterior calculus method for simulating wave equations on manifolds, extending traditional flat-space approaches to curved spaces with stability and error analysis.

Contribution

It introduces a novel DEC-based approach for wave simulation on manifolds, broadening the applicability of numerical methods beyond flat domains.

Findings

The DEC method successfully simulates wave equations on manifolds.

Stability conditions for the DEC method are established.

Error analysis confirms the method's accuracy.

Abstract

The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of discrete exterior calculus method for numerical simulation of wave equation. The advantage of this method is that it can be used to compute equation on the space manifold and the time. The analysis of its stable condition and error is also accomplished.